Advanced Digital Signal Processing (graduate)

The course focuses on Advanced Statistical Digital Signal Processing and covers the following topics:

  • Review of basics & fundamentals (8h): linear algebra & factorizations (Tel); z trasf. & filters, random processes (Mat); multivariate Gaussian (All); constrained optimization (Tel).
  • Block-processing (6h): regression, filtering, interpolation, direct & inverse problems
  • Estimation theory and performance limits (24h): Min Var. & BLUE, LS, MLE for Gaussian distributions and hints on non-Gaussians, Cramer Rao Bound, numerical examples: regression, sinusoids & PLL, TOA, xIxO identification and deconvolution.
  • Bayesian estimators (14h): a-posteriori estimation (MAP, MMSE and LMMSE); Wiener filter; linear prediction, Yule-Walker equations and Levinson recursion; EM method (2h).
  • Adaptive MMSE filters (8h): iterative LMMSE, LMS, RLS methods; examples on adaptive identification, deconvolution, and MIMO systems.
  • Bayesian tracking (8h): dynamic model and Kalman filter; examples on target positioning (e.g., GPS) & tracking.
  • Spectral analysis (10h): periodogram; parametric methods (MA, AR, ARMA models); line spectra and high-resolution methods (HOYW, MUSIC).
  • Array processing (6h): narrowband model definition, direction of arrivals (DOA), beamforming methods and multichannel systems.
  • Pattern and sequence recognition (10h): supervised and unsupervised classification, classification of signals in noise, linear discriminant, clustering methods.
  • Montecarlo simulation and numerical analysis